I honestly don't know WHY you're getting different results, but I can suspect the metering mode may be playing a role. You might try different metering modes.
The built-in metering system uses light reflected into the camera and then makes an assumption about the average reflectivity of a scene to guess how much 'actual' light exists. If you used an incident light meter (This is a separate hand-held light meter and not part of your camera. Rather than pointing it at the scene, you walk into the scene and hold the light meter in front of your subject and it measures how much light is falling on the subject.) then you get a very accurate meter reading because an incident light meter isn't fooled by the wildly variable reflectivity of different subjects (white objects reflect more light than black objects - even when those two objects are in the exact same lighting.)
The camera doesn't have an incident meter (no camera does). I only has a reflected light meter and these are somewhat easy to fool. To help, the camera has a number of different ways to sample and interpret the metering data.
You can read about Nikon's modes here:
What is the difference between Spot, Center-Weighted and Matrix Metering?
Matrix metering is using some artificial intelligence and pattern matching in an attempt to determine how best to meter the shot. It turns out this mode usually does work out fairly well... especially when you're starting out.
HOWEVER... it's not just a straight "read the meter" -> "set the exposure" metering mode.... the camera intelligence will bias the shot based on the algorithms.
In matrix metering, you have the LEAST amount of control but the computer does the MOST for you. So if you're not a pro at metering a scene, you may as well let the computer use the matrix metering mode and, more often than not, you'll get the best results. But I did preface that with "if you're not a pro at metering". Once you start to understand how metering works, you realize that you can take MORE control over the metering by switching out of matrix mode and into a different mode WHEN it's appropriate.
If you use a more basic metering mode (such as spot metering) then you can factor out the computer algorithm biasing the exposure and you may get more consistent results.
As you gain experience, you'll get better at identifying when a target is likely to give a reading which is artificially higher or artificially lower than it should be. Metering white subjects tends to cause the camera to underexpose. Metering dark/black subjects tends to cause the camera to overexpose. You learn to identify when a subject is likely to to be close to a "middle gray" value and take the metering off that element because a reflection off that surface is a more reliable indicator of the actual amount of light. Some photographers even carry a neutral gray card (12% gray) and meter the card to lock in the correct meter reading (the card has a known level of reflectivity which matches the reflectivity calibrated in the camera.)
I realize these are more advanced techniques and you just want to point your camera and get a good shot. Insight into HOW the camera works and what influences your exposures will lead to better results.